Identifying Important Nodes in Complex Networks Based on Node Propagation Entropy.

Identifying influential nodes in complex networks: Effective distance gravity model

Influential nodes refer to the ability of a node to spread information in complex networks. Identifying influential nodes is an important problem in complex networks which plays a key role in many applications such as rumor controlling, virus spreading, viral market advertising, research paper views, and citations. Basic measures like degree centrality, betweenness centrality, closeness centrality are identifying influential nodes but they are incapable of largescale networks due to time complexity issues. Chen et al. [1] proposed semi-local centrality, which is reducing computation complexity and finding influential nodes in the network. Recently Yang et al. 2020 [2] proposed a novel centrality measure based on degree and clustering coefficient for identifying the influential nodes. Sanjay et al. 2020 [3] gave voterank and neighborhood coreness-based algorithms for finding the influenced nodes in the network. Zhiwei et al. 2019 [4] considered the average shortest path to discover the influenced node in the network. These are the few recent local,global and mixed centralities. In this paper, we show a broad view of recent methods for finding influential nodes in complex networks. It also analyzes the new challenges and limitations for a better understanding of each method in detail. The experimental results based on these methods show better performance compared with existing basic centrality measures.

Accurate measurement of important nodes in complex networks has great practical and theoretical significance. Mining important nodes should not only consider the core nodes, but also take into account the locations of the nodes in the network. Despite much research on assessing important nodes, the importance of nodes in the structural holes is still easily ignored. Therefore, a local measuring method is proposed, which evaluates the nodes importance by the total constraints caused by the lack of primary structural holes and secondary structural holes around the nodes. This method simultaneously considers both the centrality and the bridging property of the nodes' first-order and second-order neighbours. Further to prove the accuracy of the method TCM, we carry out deliberate attack simulations through selective deletion in a certain proportion of network nodes. Then, we calculate the decreased ratio of network efficiency in the before-and-after attacks. Experiment results show that the average effect of the TCM in four real networks are improved by 50.64% and 14.92% compared to the clustering coefficient index and the k-shell decomposition method, respectively. Obviously, the TCM is more accurate to mine important nodes than other two methods, and it is suitable for quantitative analysis in large-scale networks.

Identifying the vital nodes in networks is of great significance for understanding the function of nodes and the nature of networks. Many centrality indices, such as betweenness centrality (BC), eccentricity centrality (EC), closeness centricity (CC), structural holes (SH), degree centrality (DC), PageRank (PR) and eigenvector centrality (VC), have been proposed to identify the influential nodes of networks. However, some of these indices have limited application scopes. EC and CC are generally only applicable to undirected networks, while PR and VC are generally used for directed networks. To design a more applicable centrality measure, two vital node identification algorithms based on node adjacency information entropy are proposed in this paper. To validate the effectiveness and applicability of the proposed algorithms, contrast experiments are conducted with the BC, EC, CC, SH, DC, PR and VC indices in different kinds of networks. The results show that the index in this paper has a high correlation with the local metric DC, and it also has a certain correlation with the PR and VC indices for directed networks. In addition, the experimental results indicate that our algorithms can effectively identify the vital nodes in different networks.

Node influence ranking in complex networks: A local structure entropy approach

Evaluating the importance of nodes in complex networks is an important topic in the research of network characteristics. Its relevant research has a wide range of applications, such as network supervision and rumor control. At present, many methods have been proposed to evaluate the importance of nodes in complex networks, but most of them have the deficiency of one-sided evaluation or too high time complexity. In order to break through the limitations of existing methods, in this paper a novel method of evaluating the importance of complex network nodes is proposed based on Tsallis entropy. This method takes into account both the local and global topological information of the node. It considers the structural hole characteristics and K-shell centrality of the node and fully takes into account the influence of the node itself and its neighboring nodes. To illustrate the effectiveness and applicability of this method, eight real networks are selected from different fields and five existing methods of evaluating node importance are used as comparison methods. On this basis, the monotonicity index, SIR (susceptible-infectious-recovered) model, and Kendall correlation coefficient are used to illustrate the superiority of this method and the relationship among different methods. Experimental results show that this method can effectively and accurately evaluate the importance of nodes in complex networks, distinguish the importance of different nodes significantly, and can show good accuracy of evaluating the node importance under different proportions of nodes. In addition, the time complexity of this method is <inline-formula><tex-math id="M2">\begin{document}$ O({n^2}) $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20210979_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20210979_M2.png"/></alternatives></inline-formula>, which is suitable for large-scale complex networks.

Measuring node importance in complex networks has great theoretical and practical significance for network stability and robustness. A variety of network centrality criteria have been presented to address this problem, but each of them focuses only on certain aspects and results in loss of information. Therefore, this paper proposes a relatively comprehensive and effective method to evaluate node importance in complex networks using a multicriteria decision‐making method. This method not only takes into account degree centrality, closeness centrality, and betweenness centrality, but also uses an entropy weighting method to calculate the weight of each criterion, which can overcome the influence of the subjective factor. To illustrate the effectiveness and feasibility of the proposed method, four experiments were conducted to rank node importance on four real networks. The experimental results showed that the proposed method can rank node importance more comprehensively and accurately than a single centrality criterion.

It is well known that protein-protein interaction (PPI) networks are typical evolving complex networks. Identification of important nodes has been an emerging popular topic in complex networks. Many indexes have been proposed to measure the importance of nodes in complex networks, such as degree, closeness, betweenness, k-shell, clustering coefficient, semi-local centrality, eigenvector centrality. Based on multivariate statistical analysis, through integrating the above indexes and further considering the appearances of nodes in network motifs, this paper aims at developing a new measure to characterize the structurally dominant proteins (SDP) in PPI networks. Moreover, we will further investigate the evolution of the defined dominant nodes in temporal evolving real-world and artificial PPI networks. Our results indicate that the constructed artificial networks have some similar statistical properties as those of the real-world evolving networks. In this case, the artificial PPI networks can be used to further investigate the above evolution characteristics of the real-world evolving networks. Simulation results reveal that SDP in the yeast PPI networks are evolutionary conserved, however, the undominant nodes evolve rapidly. Furthermore, PPI networks are very robust against random mutations, while fragile yet with certain robustness to targeted mutations on SDP. Our investigations shed some light on the future applications of the evolving characteristics of bio-molecular networks, such as reengineering of particular networks for technological, synthetic or pharmacological purposes.

Abstract. Connecting points of interest through a well-planned, inter-connected network provides manifold benefits to commuters and service providers. In the South African context, traffic congestion has become of great concern. Given how the South Africa community is slowly developing towards the use of multi-modes of mobility, the Gautrain network can be used to promote the use of multi-modes of mobility, as the Gautrain has been identified as the backbone of mobility within the Gauteng province. Currently commuters have the option to board the Gaubus (a form of Bus Rapid Transit) at their origin points which will take them to the Gautrain station to board the Gautrain. The problem to be solved arises when a commuter wishes to traverse from any bus stop to the Gautrain station, currently he/she only has one option and if the bus network has a shutdown at any point in the network the commuter’s journey will not be possible. In solving this problem, we consider the problem of graph robustness (that is creating new alternative routes to increase node/bus stop connectivity). We initial use Strava data, to identify locations were cyclist prefer to cycle and at what time of day. In graph theory, the nodes with most spreading ability are called influential nodes. Identification of most influential nodes and ranking them based on their spreading ability is of vital importance. Closeness centrality and betweenness are one of the most commonly used methods to identify influential nodes in complex networks. Using the Gaubus network we identify the influential nodes/ bus stops, using the betweenness centrality measure. The results reveal the influential nodes with the highest connectivity as these have cross-connections in the network. Identification of the influential nodes presents an important implication for future planning, accessibility, and, more generally, quality of life.

The identification of critical nodes in the network is of great significance for the research of the invulnerability and structural stability of complex networks. Most of the existing studies evaluate the importance of nodes in networks from a single structural perspective. Considering the local and global characteristics of the network, an identification algorithm of critical nodes in complex networks based on comprehensive topological importance (CTI) is proposed. The algorithm uses the theory of multiple attribute decision making (MADM) to quantitatively analyze the influence of different attributes on nodes and determine the comprehensive topology importance of nodes, which represents their structural importance in complex networks. Based on two simulation networks and five classical real networks, the proposed algorithm is proved to be superior to DC, LLS, P and WL indexes based on local information and BC indexes based on global information through the change of network efficiency under critical nodes attacking.

The identification of influential nodes in complex networks is one of the most exciting topics in network science. The latest work successfully compares each node using local connectivity and weak tie theory from a new perspective. We study the structural properties of networks in depth and extend this successful node evaluation from single-scale to multi-scale. In particular, one novel position parameter based on node transmission efficiency is proposed, which mainly depends on the shortest distances from target nodes to high-degree nodes. In this regard, the novel multi-scale information importance (MSII) method is proposed to better identify the crucial nodes by combining the network’s local connectivity and global position information. In simulation comparisons, five state-of-the-art algorithms, i.e. the neighbor nodes degree algorithm (NND), betweenness centrality, closeness centrality, Katz centrality and the k-shell decomposition method, are selected to compare with our MSII. The results demonstrate that our method obtains superior performance in terms of robustness and spreading propagation for both real-world and artificial networks.

Identifying important nodes in complex networks is a fundamental problem in network analysis. Although a plethora of measures has been proposed to identify important nodes in static (i.e., time-invariant) networks, there is a lack of tools in the context of temporal networks (i.e., networks whose connectivity dynamically changes over time). The aim of this paper is to propose a system-theoretic approach for identifying important nodes in temporal networks. In this direction, we first propose a generalization of the popular Katz centrality measure to the family of Markovian temporal networks using tools from the theory of Markov jump linear systems. We then show that Katz centrality in Markovian temporal networks can be efficiently computed using linear programming. Finally, we propose a convex program for optimizing the Katz centrality of a given node by tuning the weights of the temporal network in a cost-efficient manner. Numerical simulations illustrate the effectiveness of the obtained results.

Finding important nodes in complex networks is an important topic. However, the location information obtained by many previous studies is not sufficient and effective, and the types of attributes applied also have limitations. Based on K-shell and gravity model, this paper proposes a node importance measurement method based on multi-attribute fusion. In this method, the objective, comprehensive evaluation of multiple attributes is obtained by the entropy weight method. Experiments on real networks show that the proposed algorithm can effectively measure the importance of nodes.

A novel method of evaluating key nodes in complex networks

ABSTRACTPurposeThis study examined how social network strength (i.e., the intensity and frequency of interactions within one's personal network, assessed using centrality measures such as degree, closeness, betweenness, and eigenvector centrality) affects mental health.MethodsThe study was conducted with 108 first‐year university students. Data were collected using a structured questionnaire, and NetMiner 4.0 was employed to analyze degree centrality, closeness centrality, betweenness centrality, and eigenvector centrality as indicators of social network centrality. Additionally, Quadratic Assignment Procedure (QAP) correlation analysis and QAP regression analysis were conducted to assess the relationship between social network strength and mental health.ResultsThe study found that stronger social networks were linked to better mental health in late adolescence. Specifically, higher social network centrality was associated with lower levels of hopelessness and depression. QAP correlation analysis revealed that hopelessness had a significant negative correlation with in‐closeness centrality (which reflects how easily one can be reached by others within the network) (r = −0.252, p < 0.05), while depression was negatively correlated with in‐degree centrality (the number of direct incoming connections from peers) (r = −0.233, p < 0.05), in‐closeness centrality (r = −0.256, p < 0.05), and eigenvector centrality (a measure of how well a person is connected to popular or influential members of the network) (r = −0.291, p < 0.01). QAP regression analysis further confirmed that weaker social ties, indicated by higher out‐closeness centrality (how easily one can reach others, especially those at a distance), were associated with higher depressive symptoms (adj. R2 = 0.143, F = 2.423, p < 0.05). These results suggest that building stronger and more integrated social networks may help reduce psychological distress and support mental well‐being in late adolescence.ConclusionStronger social networks in late adolescence are associated with better mental health, highlighting the importance of social connections. While correlational findings suggest general links between centrality and emotional well‐being, the regression results underscore specific predictors with practical implications. In‐degree, in‐closeness, and eigenvector centrality were associated with reduced depressive symptoms, indicating that being well‐integrated within a social network may offer protective benefits. In contrast, high out‐closeness centrality predicted increased depression, suggesting that the effort required to maintain outward‐reaching connections may impose psychological burdens. These findings suggest that targeted interventions should focus on strengthening inward social integration while addressing the stress related to maintaining extensive outward connections, providing direction for more effective youth mental health strategies.